To assess the effect of piston ring type and oil type on piston ring wear, three types of piston ring and four types of oil were studied. Three replications of an experiment, in which the number of milligrams of material lost from the ring in four hours of running was measured, were carried out for each of the 12 combinations of oil type and piston ring type. With oil type as the row effect and piston ring type as the column effect, the following sums of squares were observed: SSA = 1.0926, SSB = 0.9340, SSAB = 0.2485, SSE = 1.7034. a) How many degrees of freedom are there for the effect of oil type? b) How many degrees of freedom are there for the effect of piston ring type? c) How many degrees of freedom are there for interactions? d) How many degrees of freedom are there for error? e) Construct an ANOVA table. You may give ranges for the P-values. f) Is the additive model plausible? Provide the value of the test statistic and the P-value. g) Is it plausible that the main effects of oil type are all equal to 0? Provide the value of the test statistic and the P-value. h) Is it plausible that the main effects of piston ring type are all equal to 0? Provide the value of the test statistic and the P-value.
To assess the effect of piston ring type and oil type on piston ring wear, three types of
piston ring and four types of oil were studied. Three replications of an experiment, in which
the number of milligrams of material lost from the ring in four hours of running was
measured, were carried out for each of the 12 combinations of oil type and piston ring type.
With oil type as the row effect and piston ring type as the column effect, the following sums
of squares were observed: SSA = 1.0926, SSB = 0.9340, SSAB = 0.2485, SSE = 1.7034.
a) How many degrees of freedom are there for the effect of oil type?
b) How many degrees of freedom are there for the effect of piston ring type?
c) How many degrees of freedom are there for interactions?
d) How many degrees of freedom are there for error?
e) Construct an ANOVA table. You may give
f) Is the additive model plausible? Provide the value of the test statistic and the P-value.
g) Is it plausible that the main effects of oil type are all equal to 0? Provide the value of
the test statistic and the P-value.
h) Is it plausible that the main effects of piston ring type are all equal to 0? Provide the
value of the test statistic and the P-value.
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